Let's be honest - for that much money things will be close if you aren't doing the work yourself. If a person is installing for you, then they likely will want to be providing the projector and screen to you (which makes sense) and they will have a fair bit of labor (20+ hours) to run 5.1 or 7.1 retrofit wiring through the walls and ceiling for the projector along with the easier tasks of actual projector mounting and screen hanging.
The absolute hardest part of all of this is the wire runs, and you can look to spend about $1,500+ on the labor for that portion.
Then you have a DECENT 1080p projector, such as the aforementioned Panasonic, though the 1080p/24 comment was incorrect as the Espson 1080UB handles this as well (with 2:2 pulldown) and several other similarly priced projectors do a fair job as well. The Epson is one of the more highly rated models for sure.
The screen... Well, most installers lean towards Dalite and Draper which will run about $1,500 - $2,000 for an appropriate size.
Now, if you were to go online and go with a Carada screen then your pricing and mileage may very dramatically - but most installers aren't out to give up their profit from sales to the Internet and you may run into a person who will raise labor rates, or walk away if you start doing this. I know, that is the point I am at when dealing with customers, as Internet pricing is great for the DIY guy, but completely unrealistic for those who want professionals to specify and install everything for them... and go cheap.
Likely:
$3,000(ish) for projector
$1,500(ish) for screen (of quality)
$1,500(ish) for labor
Plan to add several hundred dollars (minimum) for parts including speaker wire runs, projector wire runs, and misc. items such as back boxes and mounting hardware.
Likely will be more in the $7,000 range when all is said and done for 1080p from most installers... at the very least.
I know my pricing would put it right around $6,000 - but that would almost be a cheapest possible price getting you everything, so I'm not sure if you are likely to find something much less unless you luck out with a guy who tells you to buy everything online and does the labor for cheap. Not always the case, and often an indicator of an installer that may not know what the heck he is talking about.
A good installer will talk to you about lighting, painting, seating distance, screen size, screen color, projection placement, equipment placement, remote controls, existing equipment, future compatibility, proper wiring, conduit, patching, electrical, lighting control, universal remotes, etc. If they aren't discussing this with you, then they aren't experts leading you to a solution, but are order takers.
